Special Report on Calculator Research Released

Announcing the release of the special report, Calculators and Math Reasoning Skills in Primary Students: Moot Point Without Skilled Math Teachers.

The National Council of Teachers of Mathematics (NCTM) has gone on record recommending use of calculators in the earliest grades, thereby precipitating a debate on such use within the academic community and among school-based practitioners. In this survey of studies, research critiques, case studies, and editorials, the most generous conclusion to be drawn is that calculator usage need not hinder the development of math reasoning skills, but it may in fact do so. Educators should not be expected to adopt NCTM recommendations based on such skimpy research.

NCTM’s recommendation that calculators should be introduced under the guidance of skilled teachers is inadequate given the documented shortage of skilled math teachers at even the primary level. Until the first prerequisite is met, that is, upgrading the quality of math instruction by upgrading the quality of math teachers, the issue of calculator use in the earliest grades is largely irrelevant to math achievement, math reasoning skills, or problem solving skills.

This special 78-page report reviews a huge selection of published sources on calculator use in elementary schools. What does the research really say? Read this special report to find out.

See the sidebar for ordering instructions.

Discovery Good, Lecture Good, Too

Lecture doesn't have to be a dirty 7-letter word. One of the things we are learning about education is that we do not know what we think we know. See the new research on learning styles. Another surprise: lecture is not necessarily bad. Check out this powerful lecture method.




Sometimes lecture is not only the most effective, but also the preferred medium. Honestly, has anyone else sat through a three-hour “hands-on” professional development workshop, only to walk out wishing the presenter had lectured the material and saved everyone two and a half hours. We could have gotten some serious grading done instead.

TED:Ideas Worth Spreading relies on lectures with a strict twenty-minute limit. Some of the most effective talks last less than five minutes. It stands to reason that direct instruction, a time-honored method, has to work. It is fashionable to deride lecture as the tool of choice for control freaks. However, nobody considers the TED presenters domineering.

Why do people persist in framing every issue as a polar dichotomy? Left-right, phonics-whole language, direct instruction-constructivism. Dichotomies close down possibilities that are more likely to lead to effective strategies. With phonics-whole language, the common sense approach turns out to be the best. Phonics is a powerful tool for decoding the words students need to comprehend in order to derive the maximum benefits of whole language.

Likewise, when researchers compare direct instruction with constructivism, direct instruction generally gets the nod. When adults are the audience, direct instruction usually means old-fashioned lecture. Few classrooms actually exhibit a separation between direct instruction and constructivism. Most teachers blend both approaches every day for maximum effective learning.

For more Power Teaching videos, search "power teaching" in the YouTube search window. Notice how well prepared the teacher is. He has written everything on the board before he began. I tried out the technique this past summer in a "Finance 4 Kids" class with mixed results, probably because I need more practice. The students were receptive and active. Here is a less intense example of Power Teaching, also known as “whole brain teaching.”

Review of Rosetta Stone

There are any number of online reviews of the popular language learning program, Rosetta Stone. Reviews are mixed. Some reviewers love the product, other loathe it. At around $500, nearly everyone complains about its high cost.

Most reviewers evaluate software as consumers, and their input is valuable. However, they generally have no linguistic training or foreign language teaching experience to inform their reviews. I would like to contribute to rectifying the lack of professional review.

Using the demo available on the Rosetta website, I evaluated the software in several second languages that I speak with varying fluency from barely familiar to highly proficient. I also tried a couple languages from scratch.

Learning through Immersion

Most reviewers really want to learn to speak a foreign language and hope that Rosetta Stone lives up to its implied promise, that you can learn a foreign language though immersion just as easily as a child learns his native language.

The company literature exploits a common popular misunderstanding of the process of second language acquisition. Babies did not learn their native language “easily.” They typically spend a whole year or more collecting linguistic data and testing hypotheses before they even venture to try single words. Eventually, they progress to two-word utterances. It takes five years to attain the child-level fluency. Most adults want to progress a whole lot faster.

The consumer should be very happy the company has no intention of recreating a “fully immersive environment” comparable to that experienced by the totally naive child. Instead, the software begins as it should, given the premise, with single nouns. Furthermore, a linguistic adult (age 10+) brings a ton of previous understandings about language and its construction. The linguistic adult knows how language works.

Elimination of Translation and Grammar Rules

In fact, many of the negative reviews hinge on the fact that Rosetta Stone purposely avoids exploiting the learner's present knowledge. The advantage adults learners possess is the ability to cut to the chase. Babies and toddlers have to encounter a bazillion instances of “add -ed to make past tense” before they can work out both the rule and the exceptions. Adults do not have the patience for a bazillion examples while they flounder.

Another major problem, once the learner proceeds beyond simple nouns to phrases and sentences is that it is not always clear what the pictures intend to convey. The sentences make sense if you already know the language. Did they say “the boy is above (or over) (or on) the airplane?” Or did they say “the boy is below (or beneath) (or under) the airplane?” In English at least, on, over, and above mean different things. Is the girl “reading” or “holding” a book? Did they say “there are three flowers (or did they mean roses)?” Or did they say “the flowers (or maybe roses) are red?”


Carefully Designed Learning Sequence

As a curriculum designer, I found serious flaws with the sequence of learning. The design is a one size fits all languages, cookie cutter model. It does not matter which language, the course presents the learner with the exact same series of pictures and sentences. An appropriate sequence in one language will very likely be inappropriate in another. Of course, the advantage of this approach is that one Rosetta Stone course can serve as an translation key for any other Rosetta Stone course. Once I had gone through the Japanese (a language I already know) demo, I “understood” the Turkish (a language I had never heard before) demo.

One thing second language learners discover quickly is that languages are equal only in the most rudimentary way. For example, the word the Japanese would use for a cookie is also applied to other treats English speakers would never call a cookie. Chinese has a word for “comfortable” but Japanese does not. What is a simple conjugation in one language may be multi-syllabic or non-existent in another. For example, did you know that Japanese conjugates its adjectives?

Another flaw with the sequence is the worthlessness of some of the sentences. The language learner who ever has a reason to say “the boy is under the airplane” would more likely be screaming and pointing, and would have forgotten that sentence entirely. Just speaking for myself, in my whole life, I have never had an occasional to say, “the woman is jumping off the ladder.”

Rosetta Stone has a terrible customer service reputation. I had originally composed this post with links and blockquotes. The reports of some of Rosetta Stone's draconian practices alarmed me. After reading their terms of agreement, I decided the terms were not reviewer friendly. I removed all links and blockquotes. I cannot recommend Rosetta Stone.

*Gratuitous disclosure: No one has paid me to review Rosetta Stone.

No Evidence for Learning Style Optimization. Educational Apocalypse?

Cognitive scientists* reviewed over a thousand studies, but first, they thought it necessary to give the reading public a primer on basic research design. In the abstract no less.

First, students must be divided into groups on the basis of their learning styles, and then students from each group must be randomly assigned to receive one of multiple instructional methods. Next, students must then sit for a final test that is the same for all students. Finally, in order to demonstrate that optimal learning requires that students receive instruction tailored to their putative learning style, the experiment must reveal a specific type of interaction between learning style and instructional method: Students with one learning style achieve the best educational outcome when given an instructional method that differs from the instructional method producing the best outcome for students with a different learning style. In other words, the instructional method that proves most effective for students with one learning style is not the most effective method for students with a different learning style.

The learning style theory is so ubiquitous and so taken for granted, we sometimes forget how research is supposed to support education philosophy and practice. There is not a single education student who does not “know” they need to tailor their lessons to the particular learning styles of their students.

“Proponents of learning-style assessment contend that optimal instruction requires diagnosing individuals' learning style and tailoring instruction accordingly.

Sounds great, but now I feel empowered to confess a deep dark secret. As a classroom teacher, even now with over three decades of experience, I was never sure what learning style went with which kid. So I covered my bases. I made sure my lessons incorporated a mix of learning styles. Something for everyone.

My confession is even more damning. When I tutored one-on-one, I still could never be sure. Again, I covered my bases, going at the same material with a variety of approaches. When the light bulb snapped on, I never knew if it was because I had, at that moment, managed to match learning styles. So many variables...not enough control.

Exactly how was I supposed to determine individual learning styles. The diagnostic instruments may employ fancy verbiage, but it all boils down to one simple method: ask the student.

Assessments of learning style typically ask people to evaluate what sort of information presentation they prefer...Our review of the literature disclosed ample evidence that children and adults will, if asked, express preferences about how they prefer information to be presented to them.

Ask the student? Gee, to think all these years I had been racking my brain, observing students and trying to draw valid conclusions so I could teach them the way they learn best when all I had to do was ask them?

The only problem is education has put the pedagogical cart before the research horse.

Although the literature on learning styles is enormous, very few studies have even used an experimental methodology capable of testing the validity of learning styles applied to education.

Besides, it is entirely possible students do not know their learning style.

Moreover, of those that did use an appropriate method, several found results that flatly contradict the popular meshing hypothesis.

Nevertheless, it is premature to abandon learning styles.

However, given the lack of methodologically sound studies of learning styles, it would be an error to conclude that all possible versions of learning styles have been tested and found wanting; many have simply not been tested at all. Further research on the use of learning-styles assessment in instruction may in some cases be warranted, but such research needs to be performed appropriately.

How many other “facts” of education are open to dispute? How might these unexamined “facts” be undermining true education reform?



*Learning Styles: Concepts and Evidence. Harold Pashler, Mark McDaniel, Doug Rohrer, Robert Bjork. Psychological Science in the Public Interest. Volume 9, Issue 3, Pages 105-119. © 2009 Association for Psychological Science.

Teachers with Masters Degrees Not Worth Their Pay?

Schools are having trouble paying the bills. The extra pay teachers get for having a Masters degree costs schools nearly $9 billion per year. One college of education, the University of Washington, has proposed a strategy: “decoupling” extra pay for teachers who earn Master's degrees. Besides, what are the schools getting for the extra pay? By all accounts, teachers with Master's degrees do not get any more academic achievement out of their students than teachers not so well endowed.

Not surprisingly, the recommendation went over like the proverbial lead balloon. In fact, the original link has disappeared.

The authors expected push back from teachers, and got it. However, it was the the reaction of their colleagues from other colleges of education that seemed to take the authors most by surprise. Think of the revenue the colleges of education would lose. If teachers do not get paid for their Masters degrees, maybe they will not bother to enroll for Masters programs.

Okay, first, I would not like to think that the colleges of education would even come close to suggesting fixing their research recommendations around self-interested revenue considerations. Nope, I would not like to think that. So I will put that thought away for the moment and press on.

The University of Washington researchers concluded that students of teachers with Masters degrees in math or science posted achievement gains. Strangely, a separate study found teachers with degrees in math or science had no advantage, at least at elementary and middle school levels. No wonder practicing teachers declare a pox on all their houses. Guidance from the ivory towers is pretty fuzzy.

The University of Washington researchers believe that part of the problem is 90% of Masters degrees are in education, and everybody knows how worthless those degrees are, including the teachers who hold those them. You can hardly spend five minutes in a teacher's lounge without hearing someone complain about what a waste of time, educationally speaking, their Masters was. But at least there is the monetary compensation.

The researchers have an answer. They suggest tying extra pay to student outcomes as if they have completely missed the merit pay debates swirling around them. The most common, yet questionable, proxy for student achievement is test scores. Teachers have no control over many of the variables that influence academic achievement. Merit pay proposals perennially fail on the question of equitably evaluating teacher efficacy. The study authors would convert Masters pay into merit pay. Furthermore, colleges of education must surely bear some responsibility for the worthlessness of their Masters degrees.

But I see the issue another way. In my experience, it is usually successful, practicing teachers who go back to school for their Master's degrees. They have already proven themselves in the classroom. So it is not surprising that research fails to correlate increased academic achievement (whatever that is) with acquisition of a Masters degree. The chronology is backwards.

I do not begrudge teachers their “masters pay bump.” When it come to education, society has arrived at very little consensus on anything, except agreement that teachers are paid too little. If schools want to save money, they might start by laying off a few overpriced and unnecessary administrators. I know of a county with population 50,000 and eleven separate one-school districts with enrollments around 150 pupils per “district.” Each “district” has four expensive administrators: superintendent, assistant superintendent, principal, and vice principal. Talk about overkill.

Another thing the researchers do not understand is that the Masters degree can become a mill stone around the necks of teachers who change districts. It may even render them virtually unemployable. Schools routinely reject the applicants with the most education and experience. I have advised graduate students that if they get a Masters, they better plan on never leaving their district.

Stand and Deliver? No, Sit Down and Shut Up

The movie, Stand and Deliver, told the inspirational story of one teacher's success in using Advanced Placement (AP) calculus with his demoralized students. The students complained, worked hard, fought back, bought in, and eventually passed the AP calculus test. Test administrators thought the students had cheated and canceled their scores. The students retook—and passed---the test. Garfield High in Los Angeles would never be the same. Or would it?

Texas hopes to replicate Jaime Escalante's resounding success. More and more schools are offering more and more AP courses to more and more students. But Texas school officials do not like the results. At least they do not like the statistics. More and more students are failing.

But the latest data show Texas high school students fail more than half of the college-level exams, and their performance trails national averages.

School officials wring their hands and wonder what could be going wrong. The students who are expected to fail are failing, and surprise, students from elite schools, the top tier, are failing in increasing numbers, too.

But high failure rates from some of the Dallas area's elite campuses raise questions about whether our most advantaged high school students are prepared for college work.

What is the problem?

For one, you can not just “helicopter-drop” AP courses into a school and expect instant education reform.

Because, two, the teachers may not be qualified to teach AP courses.

So, three, the teachers tend to fail to cover the material and properly prepare the students.

Besides, four, too many students enroll without adequate academic foundation for the courses.

The problem with looking to a movie for direction in education reform is that Garfield High's AP calculus program was just a bit little different than the movie version. Mr. Escalante spent years preparing the students, requiring them to take summer courses and come to school from 7:00 am- noon on Saturdays.

Even Garfield High did not sustain their own success. Please read that link. Mr. Escalante's experience is emblematic in terms of reform obstructionism, professional jealousy, and society's lack of respect for teachers.

Algebra in 2nd Grade?

In February, 2009 a teacher in Montana made EdWeek headlines because she was teaching algebra to second graders and had been doing so for five years. Why all the oohs and aahs?


Elementary math is supposed to prepare students for high-level math classes in middle and high school. Students should not need a dedicated pre-algebra class. When I was a kid, pre-algebra did not exist. Now it is part of every school's math course line-up.

The author of a pre-algebra text wants students to build math reasoning skills. However math reasoning often does not happen. Many teachers treat pre-algebra as a last chance for students to get those blind elementary math procedures down pat. Problem is, a student can be A+ in procedures and still not understand algebra. In fact, students competent with procedure often believe they are good at math. It is not their fault. Our education system has been telling them for years that grades equal understanding. So if they get a good grade in math, naturally they conclude they are good at math.

Math has been misnamed. What passes for math in schools is often non-math. “Carry the one” is not a mathematical explanation for what happens in addition. It is a blind procedure. Students get good grades in non-math believing it is math. No wonder algebra is such a shock. Math reasoning skills actually matter in algebra.

Still a student with a good memory can get by, at least until they meet a new math monster, calculus. However, since middle and high school math also fail to teach math reasoning, now students take pre-calculus, another relatively recent addition to course offerings. Without a major change of emphasis, pre-calculus prepares students no better for calculus than pre-algebra prepared them for algebra.

By now pre-calculus students have so internalized non-math that they complain to the instructor, “Just tell us how to get the answer. We don't want to know why.” Just give us some more blind procedures.